An example of a Hilbert ring with maximal ideals of different height

Roberts, Leslie G.

doi:10.1090/S0002-9939-1973-0313234-5

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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An example of a Hilbert ring with maximal ideals of different height
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by Leslie G. Roberts PDF

Proc. Amer. Math. Soc. 37 (1973), 425-426 Request permission

Abstract:

An example is given of an integral domain which is a Hilbert ring of Krull dimension two but has some maximal ideals of height one.

References

Anthony V. Geramita, Maximal ideals in polynomial rings, Proc. Amer. Math. Soc. 41 (1973), 34–36. MR 318123, DOI 10.1090/S0002-9939-1973-0318123-8
Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
Wolfgang Krull, Jacobsonsche Ringe, Hilbertscher Nullstellensatz, Dimensionstheorie, Math. Z. 54 (1951), 354–387 (German). MR 47622, DOI 10.1007/BF01238035